bibkey: descamps2024stabilizer authors: Éloi Descamps, Borivoje Dakić year: 2024 title: “On the stabilizer formalism and its generalization” doi: 10.1088/1751-8121/ad8607 url: https://arxiv.org/abs/2309.09815v1 claim: “A state of N qubits is stabilized by a stabilizing set A of single-qubit unitaries when it is, up to a complex factor, the unique common +1 eigenvector of finitely many tensor products of elements of A; standard stabilizer states are those stabilized by P = {1, -1, i, -i}·{1, X, Y, Z}. The paper conjectures that every state stabilized by the binary operators A(theta, phi) = cos(theta) Z + sin(theta)(cos(phi) X + sin(phi) Y) and the identity is locally equivalent to a standard stabilizer state.” strata_touched:

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On the stabilizer formalism and its generalization

É. Descamps, B. Dakić, arXiv:2309.09815 (v1 2023-09-18, the only version); J. Phys. A: Math. Theor. 57, 455301 (2024). Subject: quant-ph.

The paper asks which stabilizing sets 𝒜 ⊂ U(d) give a useful generalized stabilizer formalism. It proves that the generalized Clifford group is trivial when 𝒜 generates a group dense in SU(d), and it analyses stabilization of qubit states by tensor products of binary operators A_{θ,φ} = cos θ σ_Z + sin θ (cos φ σ_X + sin φ σ_Y) exhaustively for two and three qubits. It then states:

\begin{conj} All states stabilized by the set $\mathcal A$ composed of binary
operators and the identity {\it i.e.}, $\mathcal{A}=\{A_{\theta,\phi},\1_2\}$,
are locally equivalent to standard stabilizer states (\textit{i.e.},
stabilized by the Pauli group
$\mathcal{P}=\{\pm 1,\pm i\}\cdot\{\1,\sigma_X,\sigma_Y,\sigma_Z\}$).
\end{conj}

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• DOI: https://doi.org/10.1088/1751-8121/ad8607 (the journal text was not read).
• URL: https://arxiv.org/abs/2309.09815v1 (source retrieved 2026-10-01): main.tex, the stabilization of a state by a stabilizing set (l. 113–119), the Pauli set (l. 127–130), local equivalence (l. 216), the binary operators (l. 225–226) and the conjecture (l. 358–360).